1. Ultimate Theoretical Models of Nanocomputers
Michael P. Frank
MIT Artificial Intelligence Lab

2. Goal of this Work
Outline a model of computation that can be used as the basis for the design of the most efficient possible computer architectures and algorithms, across a wide range of technologies and scales, from today’s technology all the way down to the nano-scale.

3. Who we are Work done as part of the MIT Reversible Computing Project
8/27/2018
Who we are
Work done as part of the MIT Reversible Computing Project
PI: Thomas F. Knight Jr.
With guidance from Norman H. Margolus
Other project members: Carlin Vieri, Matt Becker, M. Josephine Ammer, Matt DeBergalis

4. Ultimate Models of Computation
8/27/2018
Ultimate Models of Computation
Usable as basis for the design of a scalable architecture for a family of physical computer implementations in an achievable technology.
Accurately model the scaling behavior of computers as problem sizes increase.
Performance on any class of computations scales as well as for any physically possible architecture.

5. Benefits of Ultimate Models
8/27/2018
Benefits of Ultimate Models
Provides a final standard for algorithm design - best algorithms are really best.
Allows algorithm design independently of implementation technology.
Performance-scaling predictions remain valid as technology improves and problem sizes get larger

6. Physical Constraints Shaping the Ultimate Model

7. Limit on Processing Rate in Irreversible Computers
A - min. area of enclosing surface F - max. rate entropy flux per area S - min. entropy generated per op r - total rate of operation per time FA S
r =
Processing rate scales with surface area, not volume
S can never be less than 1 bit, per bit irreversibly erased by an operation
F limited by temp. and energy density

8. Reversible Logic Devices
Logically reversible
Asymptotically physically reversible
Entropy per op proportional to speed
Entropy per time quadratic in speed
Large variety of implementation technologies with this behavior.
Entropy coefficient or “badness” b varies widely.
S = b t
S / t = b / t 2

9. Limit of Processing Rate in Reversible Machines
Entropy per operation S = b / t
Rate entropy generation R = nS / t
Number of devices n = d / V
Total rate of operation r = n / t
Surface area (square side) A = d
Entropy removal rate R = FA d V 3 r A
d F =
b V 2 2
Beats irreversible r/A = F/S when d > FbV / S

10. Spreading things out If algorithm requires no communication:
Spread out processors arbitrarily
No speed advantage to reversibility
Still, less energy dissipated per op.
If alg. requires local communication, delay ~ cycle time, N  N  N array
Irreversible t = (N ), reversible t = O(N ).
Reversible advantage only O(N )
1/3
1/4
1/12

11. A Proposed Ultimate Architecture
3-D mesh of reversible PEs, each with:
Fixed CPU made of reversible logic devices
Fixed-size reversible memory
Variable speed of operation
Include bounded-flux networks for:
Communication
Entropy removal (cooling)
Power delivery

12. Caveats:
May not scale as well as analog systems considered as computers (e.g. wind tunnels)
Neglects possibility of quantum coherent computation
Not yet known to be scalable
Model can be extended to include it if needed
Ignores effects of gravity
At sufficiently large scales, scaling laws change

13. Algorithmic Issues At worst, simulate irreversible machine.
Array simulations of 3-D reversible systems
No production of computational entropy.
Run strictly faster on the reversible mesh.
For other applications: benefits unclear
Cost of uncomputing information may exceed benefits of 3D
Best algs for some problems may be 2D irrev.

14. Entropy transport (cooling) technologies
Max entropy flux F, bit sec^-1 cm^-2:
1 mm^2, 1 Gb/s optic fiber: 10^13
Passive emission 100W, 1cm^2, T>300K: 3x10^22
Drexler fractal plumbing, 10 kW/cm^2, T=273K: 3.8x10^24
1 1 m/s: 10^26
1 0.1 c: 10^33

15. Entropy generation in irreversible technologies
Entropy per operation S, in bits:
0.5 um 300K: 10^8
Best modern CMOS, 1/2 CV^2 = 10^-14 <900K: 10^6
Likharev’s superconducting logic, 10^ x10^4
Lowest possible: 1 bit, per bit irreversibly lost

16. Entropy coefficients of reversible technologies

17. Scales above which reversible computing is a win

18. MIT Reversible Computing Project - What We’re Doing
Design & fab a complete reversible RISC-style processor.
Reversible memory.
Resonant energy-recovery power supplies.
Reversible high-level language & compiler
Reversible algorithms and applications

19. What’s Next Prototype reversible mesh computer
for fast physical simulations
Develop efficient algorithms for a variety of problems
Need a high-level programming model for physical algorithms
Reversible manufacturing?